LEADER 04143nam 22006855 450 001 9910731479103321 005 20251008151941.0 010 $a3-031-28949-8 024 7 $a10.1007/978-3-031-28949-1 035 $a(MiAaPQ)EBC7262699 035 $a(Au-PeEL)EBL7262699 035 $a(DE-He213)978-3-031-28949-1 035 $a(PPN)272267244 035 $a(CKB)27082641300041 035 $a(MiAaPQ)EBC7262690 035 $a(EXLCZ)9927082641300041 100 $a20230616d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aC*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics $eAn Introduction /$fby Jean-Bernard Bru, Walter Alberto de Siqueira Pedra 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (497 pages) 225 1 $aLatin American Mathematics Series ? UFSCar subseries,$x2524-6763 311 08$aPrint version: Bru, Jean-Bernard C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics Cham : Springer International Publishing AG,c2023 9783031289484 320 $aIncludes bibliographical references and index. 327 $aPreface -- Ordered vector spaces and positivity -- The space of bounded operators on a Hilbert space as ordered vector space -- Thermodynamic equilibrium of finite quantum systems -- Elements of C*-algebra -- Thermodynamic equilibrium in infinite volume -- Equilibrium states of mean-field models and Bogolioubov's approximation method -- Appendix -- References -- Index. 330 $aThis textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics. It presents a conceptually profound yet technically accessible path to the C*-algebraic approach to quantum statistical mechanics, demonstrating how key aspects of thermodynamic equilibrium can be derived as simple corollaries of classical results in convex analysis. Using C*-algebras as examples of ordered vector spaces, this book makes various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory much clearer from both mathematical and physical perspectives. It begins with the simple case of Gibbs states on matrix algebras and gradually progresses to a more general setting that considers the thermodynamic equilibrium of infinitely extended quantum systems. The book also illustrates how first-order phase transitions and spontaneous symmetry breaking can occur, in contrast to the finite-dimensional situation. One of theunique features of this book is its thorough and clear treatment of the theory of equilibrium states of quantum mean-field models. This work is self-contained and requires only a modest background in analysis, topology, and functional analysis from the reader. It is suitable for both mathematicians and physicists with a specific interest in quantum statistical physics. 410 0$aLatin American Mathematics Series ? UFSCar subseries,$x2524-6763 606 $aMathematical physics 606 $aStatistical mechanics 606 $aQuantum theory 606 $aFunctional analysis 606 $aMathematical Physics 606 $aMathematical Methods in Physics 606 $aStatistical Mechanics 606 $aQuantum Physics 606 $aFunctional Analysis 615 0$aMathematical physics. 615 0$aStatistical mechanics. 615 0$aQuantum theory. 615 0$aFunctional analysis. 615 14$aMathematical Physics. 615 24$aMathematical Methods in Physics. 615 24$aStatistical Mechanics. 615 24$aQuantum Physics. 615 24$aFunctional Analysis. 676 $a905 700 $aBru$b Jean-Bernard$0823048 702 $aAlberto de Siqueira Pedra$b Walter 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910731479103321 996 $a-Algebras and Mathematical Foundations of Quantum Statistical Mechanics$94450690 997 $aUNINA